A pharmacist attempts to weigh 0.365 g of morphine sulfate on a balance of dubious accuracy. When checked on a highly accurate balance, the weight is found to be 0.390 g. Calculate the percentage of error in the first weighing. (Note: Round the answer to one decimal place).
Choose the best answer

A) 6.7%

B) 6.3%

C) 5.9%

D) 5.5%

To calculate the percentage error in the first weighing, we use the following formula for percentage error:

\[
\text{Percentage Error} = \left( \frac{\text{True Value} - \text{Measured Value}}{\text{True Value}} \right) \times 100
\]

### Given:
- **Measured Value** (initial weighing) = 0.365 g
- **True Value** (accurate weighing) = 0.390 g

Substituting the values into the formula:

\[
\text{Percentage Error} = \left( \frac{0.390 - 0.365}{0.390} \right) \times 100
\]

Let's calculate it.The percentage error in the first weighing is approximately **6.4%**. However, this answer doesn't match any of the provided options exactly.

The closest option is **B) 6.3%**. Therefore, **B** is the best answer.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How would the percentage error change if the measured value was higher than the true value?
2. What is the difference between absolute error and percentage error?
3. How can a pharmacist ensure a balance is accurate for precise measurements?
4. What other factors can affect the accuracy of a balance?
5. How does percentage error differ from standard deviation in error analysis?

**Tip:** Always calibrate balances with certified weights to minimize measurement errors.

Learn how to calculate the percentage error in weighing 0.365 g of morphine sulfate compared to a true value of 0.390 g. Understand the formula and steps involved in determining percentage error for accurate measurement. Suitable for high school students studying measurement and error analysis.

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